Apparatus and method for image processing, and program for use therein, and learning apparatus

ABSTRACT

The present invention provides an image processing apparatus for converting a first image into a second image having higher image quality than that of the first image, includes: a first pixel value extracting section; an estimate noise amount arithmetically operating section; a processing coefficient generating section; a second pixel value extracting section; and a predicting section.

CROSS REFERENCES TO RELATED APPLICATIONS

The present invention contains subject matter related to Japanese PatentApplication JP 2007-330452 filed in the Japan Patent Office on Dec. 21,2007, the entire contents of which being incorporated herein byreference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an image processing apparatus, an imageprocessing method, and a program for use therein, and a learningapparatus, and more particularly to an image processing apparatus and animage processing method each of which is capable of removing a noise,which is generally generated and which has luminance dependency, from avideo signal corresponding to an image, and a program for use therein,and a learning apparatus.

2. Description of the Related Art

In related art, in noise removing processing for removing a noise from avideo signal corresponding to an image, the noise is treated as a whitecolor, and pixel values of the peripheral pixels are added to oneanother, thereby removing the noise from a video signal corresponding toan image.

On the other hand, in recent years, it has been devised in the noiseremoving processing that the noise is assumed to have a color becausethere is a deviation in color of the noise, and thus the noise isremoved with a high degree of accuracy as compared with the case wherethe noise is treated as the white color.

For example, it has been devised in the noise removing processing thatblack pixel signals generated in black pixels obtained bylight-shielding an opening portion are subtracted from pixel signalsoutputted from the effective pixels, respectively, thereby removing afixed pattern noise (FPN) with which the pixel signals are mixed due toa manufacturing error. This technique, for example, is descried inJapanese Patent Laid-Open No. 2007-116292. In that noise removingprocessing, in order to remove the noise due to the manufacturing error,the black pixel signals need to be detected every product.

SUMMARY OF THE INVENTION

On the other hand, it has not been devised in the noise removingprocessing to remove a noise which, for example, does not depend on anyof the manufacturing processes, but has luminance dependency which animage sensor itself generally has (hereinafter referred to as “aluminance dependency noise”).

The present invention has been made in the light of such circumferences,and it is therefore desirable to provide an image processing apparatusand an image processing method each of which is capable of removing anoise, which is generally generated and which has luminance dependency,from a video signal corresponding to an image, and a program for usetherein, and a learning apparatus.

In order to attain the desire described above, according to anembodiment of the present invention, there is provided an imageprocessing apparatus for converting a first image into a second imagehaving higher image quality than that of the first image, including: afirst pixel value extracting section for extracting a plurality of pixelvalues, within the first image, corresponding to a position of a pixelof interest, and peripheral positions of the position of the pixel ofinterest within the second image; an estimate noise amountarithmetically operating section for obtaining estimate noise amountsfor the plurality of pixel values extracted by the first pixel valueextracting section, respectively; a processing coefficient generatingsection for generating second processing coefficients in accordance withan arithmetic operation for first processing coefficients previouslylearned from a normal equation, and the estimate noise amounts obtainedfor the plurality of pixel values, respectively, within the first image,the normal equation being obtained based on a relational expression forgenerating a teacher image corresponding to the second image havinghigher image quality than that of a student image in accordance with anarithmetic operation for the second processing coefficients obtained inaccordance with estimate noise amounts about the pixel values within thestudent image corresponding to the first image, and the first processingcoefficients, and the student image; a second pixel value extractingsection for extracting a plurality of pixel values, within the firstimage, corresponding to a position of a pixel of interest, andperipheral positions of the position of the pixel of interest within thesecond image; and a predicting section for generating a pixel value ofthe pixel of interest within the second image in accordance with anarithmetic operation for the plurality of pixel values extracted by thesecond pixel value extracting section, and the second processingcoefficients.

According to another embodiment of the present invention, there isprovided an image processing method for use in an image processingapparatus for converting a first image into a second image having higherimage quality than that of the first image, the image processing methodincluding the steps of: extracting a plurality of pixel values, withinthe first image, corresponding to a position of a pixel of interest, andperipheral positions of the position of the pixel of interest within thesecond image; obtaining estimate noise amounts for the plurality ofpixel values, respectively; obtaining second processing coefficients inaccordance with an arithmetic operation for first processingcoefficients previously learned from a normal equation, and the estimatenoise amounts obtained for the plurality of pixel values, respectively,within the first image, the normal equation being obtained based on arelational expression for generating a teacher image corresponding tothe second image having higher quality than that of a student image inaccordance with an arithmetic operation for the second processingcoefficients obtained in accordance with estimate noise amounts aboutthe pixel values within the student image corresponding to the firstimage, and the first processing coefficients, and the student image;extracting a plurality of pixel values, within the first image,corresponding to a position of a pixel of interest, and peripheralpositions of the position of the pixel of interest within the secondimage; and generating a pixel value of the pixel of interest within thesecond image in accordance with an arithmetic operation for theplurality of pixel values thus extracted, and the second processingcoefficients.

According to the embodiments of the present invention described above,the plurality of pixel values, within the first image, corresponding tothe position of the pixel of interest, and the peripheral positions ofthe position of the pixel of interest within the second image having thehigher image quality than that of the first image are extracted. Theestimate noise amounts are obtained with respect to the plurality ofpixel values thus extracted, respectively. The second processingcoefficients are obtained in accordance with the arithmetic operationfor the first processing coefficients previously learned from the normalequation, and the estimate noise amounts obtained for the plurality ofpixel values, respectively, within the first image. In this case, thenormal equation is obtained based on the relational expression forgenerating the teacher image corresponding to the second image havingthe higher image quality than that of the student image in accordancewith the arithmetic operation for the second processing coefficientsobtained in accordance with the estimate noise amounts about the pixelvalues, within the student image, corresponding to the first image andthe first processing coefficients, and the student image. In addition,the plurality of pixel values, within the first image, corresponding tothe position of the noticed image, and the peripheral positions of theposition of the noticed image within the second image are extracted.Also, the pixel value of the pixel of interest within the second imageis generated in accordance with the arithmetic operation for theplurality of pixel values thus extracted, and the second processing.

According to still another embodiment of the present invention, there isprovided a program in accordance with which a computer executes imageprocessing for converting a first image into a second image havinghigher image quality than that of the first image, the program includingthe steps of: extracting a plurality of pixel values, within the firstimage, corresponding to a position of a pixel of interest, andperipheral positions of the position of the pixel of interest within thesecond image; obtaining estimate noise amounts for the plurality ofpixel values, respectively; obtaining second processing coefficients inaccordance with an arithmetic operation for first processingcoefficients previously learned from a normal equation, and the estimatenoise amounts obtained for the plurality of pixel values, respectively,within the first image, the normal equation being obtained based on arelational expression for generating a teacher image corresponding tothe second image having higher quality than that of a student image inaccordance with an arithmetic operation for the second processingcoefficients obtained in accordance with estimate noise amounts aboutthe pixel values within the student image corresponding to the firstimage, and the first processing coefficients, and the student image;extracting a plurality of pixel values, within the first image,corresponding to a position of a pixel of interest, and peripheralpositions of the position of the pixel of interest within the secondimage; and generating a pixel value of the pixel of interest within thesecond image in accordance with an arithmetic operation for theplurality of pixel values thus extracted, and the second processingcoefficients.

According to yet another embodiment of the present invention, there isprovided a learning apparatus, including: a normal equation generatingsection for obtaining estimate noise amounts from pixel values within astudent image containing therein a noise having noise dependency,obtaining second processing coefficients in accordance with anarithmetic operation for the estimate noise amounts, and firstprocessing coefficients, and generating a normal equation by using thepixel values of the student image, and pixel values of the teacherimage, in order to solve a relational expression for generating theteacher image having higher image quality than that of the studentimage, in accordance with an arithmetic operation for the secondprocessing coefficients and the student image; and a coefficientgenerating section for generating the first processing coefficients bysolving the normal equation.

According to the embodiments of the present invention described above,the estimate noise amounts are obtained from the pixel values within thestudent image containing therein the noise having the luminancedependency. The second processing coefficients are obtained inaccordance with the arithmetic operation for the estimate noise amounts,and the first processing coefficients. In addition, the normal equationis generated by using the pixel values of the student image, and thepixel values of the student image, in order to solve the relationalexpression for generating the teacher image having the higher imagequality than that of the student image, in accordance with thearithmetic operation for the second processing coefficients and thestudent image. Also, the first processing coefficients are generated bysolving the normal equation.

As set forth hereinabove, according to the present invention, the noisewhich is generally generated and which has the luminance dependency canbe removed from the video signal corresponding to the image.

In addition, it is possible to generate the processing coefficients forremoving the noise which is generally generated and which has theluminance dependency from the video signal corresponding to the image.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing a configuration of an image processingapparatus according to an embodiment of the present invention;

FIG. 2 is a graph showing light quantity dependency of amounts of noiseswhich two kinds of image sensors have, respectively;

FIG. 3 is a diagram explaining a norm for learning for predictivecoefficients;

FIG. 4 is a view showing a class tap composed of pixel values of pixelsof 3×3;

FIG. 5 is a graph showing predictive coefficients which are multipliedby pixel values composing a predictive tap;

FIG. 6 is a flow chart explaining noise removing processing executed bythe image processing apparatus shown in FIG. 1;

FIG. 7 is a diagram showing an addition matrix;

FIG. 8 is a block diagram showing a configuration of a learningapparatus for learning processing coefficients according to anembodiment of the present invention;

FIG. 9 is a flow chart explaining the learning processing executed bythe learning apparatus shown in FIG. 8; and

FIG. 10 is a block diagram showing a configuration of hardware of acomputer.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 1 is a block diagram showing a configuration of an image processingapparatus 10 according to an embodiment of the present invention.

The image processing apparatus 10 shown in FIG. 1 is composed of a classtap extracting portion 11, a class classifying portion 12, a coefficientstoring portion 13, a noise amount tap extracting portion 14, a noiseamount arithmetically operating portion 15, a predictive coefficientgenerating portion 16, a predictive tap extracting portion 17, and apredicting portion 18.

The image processing apparatus 10 executes class classifying adaptationprocessing. In the class classifying adaptation processing, a class fora pixel of interest in an output image which will be generated afterthis is generated, and predictive coefficients of the output imagehaving higher image quality than that of an input image are generatedfrom the input image by using predictive coefficients obtained based ona processing coefficient of the class, and an estimate value for anamount of noise as a variance value of a luminance dependency noise ofthe input image (hereinafter referred to as “an estimate noise amount”),and the input image.

It is noted that the processing coefficients used in the classclassifying adaptation processing executed by the image processingapparatus 10, for example, is obtained from learning (its details willbe described later) using an image containing therein the luminancedependency noise, and an image from which the luminance dependency noiseis removed. Therefore, the image processing apparatus 10 can generate animage, having high image quality, from which the luminance dependencynoise is removed by executing the class classifying adaptationprocessing. From this, the class classifying adaptation processingexecuted by the image processing apparatus 10 can be the as noiseremoving processing for removing the luminance dependency noise from theinput image as it were.

In the image processing apparatus 10 shown in FIG. 1, the class tapextracting portion 11 successively determines pixels composing an outputimage (this output image is one which will be generated after this anddoes not exist at the current stage, and thus is virtually supposed) aspixels of interest. The class tap extracting portion 11 extracts pixelvalues of a plurality of pixels, within the input image, correspondingto a position of the pixel of interest, and peripheral positions of theposition of the pixel of interest as a class tap from the input image.In this case, the pixel values of the plurality of pixels within theinput image are used to classify the pixels of interest into classes.The class tap extracting portion 11 supplies the class tap to the classclassifying portion 12.

The class classifying portion 12 classifies the pixels of interest intoclasses in correspondence to the feature of the class tap suppliedthereto from the class tap extracting portion 11, thereby generating theclasses for the pixels of interest. Adaptive dynamic range coding (ADRC)or the like, for example, can be adopted as a method of classifying thepixels of interest into the classes. With a method using the ADRC, thepixel values composing the class tap are ADRC-processed, and the classesof the pixels of interest are determined in accordance with ADRC codesobtained as the result of executing the ADRC processing. As a result,the pixels of interest are classified into the classes in accordancewith correlation (waveform) of the class tap.

Note that, in K-bit ADRC, for example, a maximum value MAX and a minimumvalue MIN of the pixel values composing the class tap are detected.DR=MAX−MIN is set as a local dynamic range of a set of a plurality ofpixel values composing the class tap. Also, each of the plurality ofpixel values as the class tap is re-quantized into K-bits based on thedynamic range DR. That is to say, the minimum value MIN is subtractedfrom each of the pixel values as the class tap, and each of theresulting values obtained from the subtraction is divided by DR/2^(K)(quantized). Also, a bit string which is obtained by arranging the K-bitdata, as the class tap, obtained in the manner described above in thepredetermined order is set as the ADRC code.

Therefore, when the class tap, for example, is subjected to 1-bit ADRCprocessing, after the minimum value MIN is subtracted from each of thepixel values as the class tap is divided by ½ of a difference betweenthe maximum value MAX and the minimum value MIN (rounding-down of afractional part). As a result, each data is set as 1 bit (binarized).Also, a bit string obtained by arranging the data of 1 bit in thepredetermined order is set as the ADRC code. The data on the classes forthe pixels of interest generated by the class classifying portion aresupplied to the coefficient storing portion 13.

The coefficient storing portion 13 stores therein the optimal processingcoefficients for the classes obtained from the learning which will bedescribed later. The coefficient storing portion 13 reads out theprocessing coefficients corresponding to the classes the data on whichis supplied from the class classifying portion 12, and supplies theprocessing coefficients thus read out to the predictive coefficientgenerating portion 16.

The noise amount tap extracting portion 14 successively determines thepixels composing the output image as the pixels of interest similarly tothe case of the class tap extracting portion 11. The noise amount tapextracting portion 14 extracts the pixel values of the plurality ofpixels, within the input image, corresponding to the position of thepixel of interest, and the peripheral positions of the position of thepixel of interest as the noise amount tap from the input image. In thiscase, the pixel values of the plurality of pixels within the input imageare used to arithmetically operate the estimate noise amountcorresponding to the pixel of interest. The noise amount tap extractingportion 14 supplies the noise amount tap to the noise amountarithmetically operating portion 15.

The noise amount arithmetically operating portion 15 arithmeticallyoperates the estimate noise amount corresponding to the pixel ofinterest from the noise amount tap supplied thereto from the noiseamount tap extracting portion 14, and supplies the resulting estimatenoise amount to the predictive coefficient generating portion 16.

The predictive coefficient generating portion 16 carries out apredetermined matrix arithmetic operation by using the processingcoefficients supplied thereto from the coefficient storing portion 13,and the estimate noise amount supplied thereto from the noise amountarithmetically operating portion 15, thereby generating the predictivecoefficients. The predictive coefficient generating portion 16 suppliesthe predictive coefficients thus generated to the predicting portion 18.

The predictive tap extracting portion 17 successively determines thepixels composing the output image as the pixels of interest similarly tothe case of each of the class tap extracting portion 11 and the noiseamount tap extracting portion 14. The predictive tap extracting portion17 extracts the pixel values of the plurality of pixels, within theinput image, corresponding to the position of the pixel of interest, andthe peripheral positions of the position of the pixel of interest as thepredictive tap from the input image. In this case, the pixel values ofthe plurality of pixels within the input image are used to predict thepixels of interest. Also, the predictive tap extracting portion 17supplies the predictive tap thus extracted to the predicting portion 18.

The predicting portion 18 carries out the predictive arithmeticoperation for predicting the pixel of interest by using the predictivecoefficients supplied thereto from the predictive coefficient generatingportion 16, and the predictive tap supplied thereto from the predictivetap extracting portion 17. As a result, the predicting portion 18generates the predictive value of the pixel value of the pixel ofinterest as the pixel value of the pixel of interest composing theoutput image. Also, the predicting portion 18 outputs the output imagecomposed of the pixel values obtained from the predictive arithmeticoperation.

Next, an arithmetic operation for the estimate noise amount by the noiseamount arithmetically operating portion 15 shown in FIG. 1 will bedescribed with reference to FIG. 2.

A graph of FIG. 2 shows light quantity (luminance) dependency of amountsof noises which two kinds of image sensors have, respectively. It isnoted that in FIG. 2, an axis of abscissa represents a total lightquantity, that is, a pixel value, and an axis of ordinate represents anamount of noise.

As shown in FIG. 2, the amounts of noises which the two kinds of imagesensors have, respectively, have the luminance dependency. Thus, theamount of noise a can be expressed in the form of a quadratic expressionof a true value L of the pixel value given by Expression (1):

σ² =aL ² +bL+c  (1)

where a, b and c are parameters inherent in the image sensor,respectively.

According to Expression (1), the amount of noise of the pixelcorresponding to the true value L of the pixel value can bearithmetically operated from the true value L of the pixel value.Therefore, the noise amount arithmetically operating portion 15 mayobtain the amount of noise by carrying out the arithmetic operation forExpression (1). Actually, however, it is impossible to acquire the pixelvalue in which the true value of the pixel value, that is, the luminancedependency noise is not contained. For this reason, the estimate noiseamount σ′ is arithmetically operated by carrying out the arithmeticoperation for Expression (2) by using a pixel value L′ containingtherein the noise:

σ′² =aL′ ² +bL′+c  (2)

Next, the class classifying adaptation processing executed in the imageprocessing apparatus 10 will be desired with reference to FIGS. 3 to 5.

When it is assumed that in the image processing apparatus 10 shown inFIG. 1, the predicting portion 18, for example, carries out a linearpredictive arithmetic operation as a predetermined predictive arithmeticoperation, the pixel value y composing the output image is obtained inaccordance with Expression (3) as a linear expression:

y=WX  (3)

where X represents an n-dimensional vector (X=(x₀, x₁, . . . , x_(n)))consisting of the n pixel values, of the n pixels of the input image,composing the predictive tap about the pixel value y of the outputimage, and W represents an n-dimensional vector (W=(w₀, w₁, . . . ,w_(n))) consisting of the predictive coefficients which are multipliedby the n pixel values of the n pixels, respectively. From the above, thenumber of pixels composing the predictive tap is equal to the number ofpredictive coefficients composing the predictive coefficient W.

However, the optical predictive coefficient W can be obtained from thelearning which will be described later. However, in order to executehighly precise noise removing processing, the following two items arerequired as the norm for the learning thereof.

A first item is such that the predictive coefficient W is changed basedon the correlation (waveform) of the predictive tap. That is to say, thefirst item is such that the predictive coefficient W which is multipliedby the pixel value is made large in that pixel value, nearer the pixelvalue of the pixel of interest, of the pixel values composing thepredictive tap.

For example, as shown on a left-hand side of FIG. 3, it is assumed thatthe predictive tap is composed of a pixel value x₁ of a pixel of aninput image corresponding to a position of a pixel of interest, a pixelvalue x₀ near the pixel value x₁, and a pixel value x₂ far from thepixel value x₁. In this case, the predictive coefficient W needs to belearned so that the predictive coefficient w₀ which is multiplied by thepixel value x₀ becomes larger than the predictive coefficient w₂ whichis multiplied by the pixel value x₂ which is located farther from thepixel value x₁ than the pixel value x₀ is located.

In addition, a second item is such that the predictive coefficient W ischanged based on the estimate noise amount σ′ of the input image. Thatis to say, the predictive coefficient W which is multiplied by the pixelvalue is made large in that pixel value having the less estimate noiseamount σ′.

For example, as shown on a right-hand side of FIG. 3, it is assumed thata predictive tap is composed of a pixel value x₁ of the pixel of theinput image corresponding to the position of a pixel of interest, apixel value x₀ having an estimate noise amount σ₀, and a pixel value x₂having an estimate noise amount σ₂ larger than the estimate noise amountσ₀. In this case, the predictive coefficient W needs to be learned sothat the predictive coefficient w₀ which is multiplied by the pixelvalue x₀ becomes larger than the predictive coefficient w₂ which ismultiplied by the pixel value x₂ having the larger estimate noise amountx₂ than the estimate noise σ₀ of the pixel value x₀.

Cluster classification learning is known as a method of learning theoptimal predictive coefficient in accordance with the norm as describedabove. In this case, with the cluster classification learning, thepixels of interest are classified into classes based on the correlationof the cluster tap, and the estimate noise amount σ′, and the predictivecoefficient is obtained every class. However, in this case, the numberof classes explosively increases, so that it becomes difficult to learnthe predictive coefficients. For example, when the class tap, as shownin FIG. 4, is composed of the pixel values of the pixels of 3×3, if thecorrelation of the class tap is represented by subjecting each of thepixel values of the pixels to the 1-bit ADRC processing, and theestimate noise amount σ′ of each of the pixels is represented by 3 bits,the total number of classes becomes about 6.9×10¹⁰ (=512×8⁹).

Thus, the optimal processing coefficient for each of the classesobtained by the classification based on the correlation of the class tapis obtained in the learning which will be described later. Also, theimage processing apparatus 10 optimizes that processing coefficient incorrespondence to the estimate noise amount σ′ in the classclassification adaptation processing, and carries out the predictivearithmetic operation with the optimized processing coefficient as thepredictive coefficient W.

That is to say, the maximum signification of the class classificationlearning is to change the value of the predictive coefficient everyclass. For example, as shown in FIG. 5, the predictive coefficientswhich are multiplied by the pixel values, respectively, within thepredictive tap are different from each other in two different classes.It is noted that in FIG. 5, an axis of abscissa represents the positionsof the pixels corresponding to the pixel values composing the predictivetap, and an axis of ordinate represents the predictive coefficientswhich are multiplied by the pixel values of the pixels, respectively.

Thus, the image processing apparatus 10 optimizes the predictivecoefficients in accordance with Expression (4) similarly to the casewhere the predictive coefficient W is changed in correspondence to theestimate noise amount σ′ based on the optimal processing coefficient foreach of the classes obtained by the classification based on thecorrelation of the class tap obtained from the learning, therebyclassifying and learning the pixels of interest based on the correlationof the class tap, and the estimate noise amounts.

$\begin{matrix}{W \cong {W_{0} + {\sum\limits_{i = 0}^{m}{\sigma_{i}^{\prime}W_{\sigma^{\prime}i}}}}} & (4)\end{matrix}$

where W₀ and W_(σ′i) are processing coefficients of an n-dimensionalvector corresponding to the predictive coefficient W of then-dimensional vector, m is the number of pixel values composing thenoise amount tap, and σ′_(i) is an estimate noise amount of an i-thpixel value within the noise amount tap. It is noted that the number, m,of pixel values composing the noise amount tap may be either identicalto or different from the number, n, of pixel values composing thepredictive tap.

In addition, Expression (4) is expressed in the form of a determinant ofmatrix as follows:

$\begin{matrix}{\begin{pmatrix}w_{0} \\w_{1} \\\vdots \\w_{n}\end{pmatrix} \cong {\begin{pmatrix}w_{0,0} \\w_{0,1} \\\vdots \\w_{0,n}\end{pmatrix} + {\begin{pmatrix}w_{{\sigma^{\prime}0},0} & \ldots & w_{{\sigma^{\prime}m},0} \\w_{{\sigma^{\prime}0},1} & \ldots & w_{{\sigma^{\prime}m},1} \\\vdots & ⋰ & \vdots \\w_{{\sigma^{\prime}0},n} & \ldots & w_{{\sigma^{\prime}m},n}\end{pmatrix}\begin{pmatrix}\sigma_{0}^{\prime} \\\sigma_{1}^{\prime} \\\vdots \\\sigma_{m}^{\prime}\end{pmatrix}}}} & (5)\end{matrix}$

where w_(0,0), w_(0,1), . . . , w_(0,n) represent n elements of theprocessing coefficients W₀ of the n-dimensional vector, respectively,and w_(σi′,0), w_(σi′,1), . . . , w_(σi′,n) represent n elements of theprocessing coefficients W_(σi′), of the n-dimensional vector,respectively.

Next, the noise removing processing executed by the image processingapparatus 10 shown in FIG. 1 will be described with reference to a flowchart of FIG. 6.

Firstly, in Step S11, the class tap extracting portion 11, the noiseamount tap extracting portion 14, and the predictive tap extractingportion 17 determine one, of a plurality of pixels composing the outputimage, which is not yet set as a pixel of interest as the pixel ofinterest. Next, in Step S12, the class tap extracting portion 11extracts the class tap corresponding to the pixel of interest from theinput image, and supplies the class tap thus extracted to the classclassifying portion 12.

In Step S13, the class classifying portion 12 classifies the pixel ofinterest into the corresponding one of the classes in correspondence tothe feature of the class tap supplied thereto from the class extractingportion 11, thereby generating the class for the pixel of interest.Also, the class classifying portion 12 supplies the data on the classthus generated for the pixel of interest to the coefficient storingportion 13.

In Step S14, the noise amount tap extracting portion 14 extracts thenoise amount tap corresponding to the pixel of interest from the inputimage, and supplies the data on the noise amount tap thus extracted tothe noise amount arithmetically operating portion 15. In Step S15, thenoise amount arithmetically operating portion 15 arithmetically operatesthe estimate noise amount σ′ corresponding to the pixel of interest fromthe noise amount tap supplied thereto from the noise amount tapextracting portion 14 in accordance with Expression (2), and suppliesthe data on the resulting estimate noise amount σ′ to the predictivecoefficient generating portion 16.

In Step S16, the coefficient storing portion 13 reads out the processingcoefficient corresponding to the class supplied thereto from the classclassifying portion 12, and supplies the processing coefficient thusread out to the predictive coefficient generating portion 16. In StepS17, the predictive coefficient generating portion 16 carries out thearithmetic operation for the matrix of Expression (5) by using theprocessing coefficients supplied thereto from the coefficient storingportion 13, and the estimate noise amounts σ′ supplied thereto from thenoise amount arithmetically operating portion 15, thereby generating thepredictive coefficient W. The predictive coefficient generating portion16 supplies the predictive coefficient W to the predicting portion 18.

In Step S18, the predictive tap extracting portion 17 extracts thepredictive tap corresponding to the pixel of interest from the inputimage, and supplies the data on the predictive tap thus extracted to thepredicting portion 18. In Step S19, the predicting portion 18 carriesout the predictive arithmetic operation for Expression (3) by using thepredictive coefficient W supplied thereto from the predictivecoefficient generating portion 16, and the predictive tap suppliedthereto from the predictive tap extracting portion 17. As a result, thepredicting portion 18 generates the predictive value for the pixel valueof the pixel of interest as the pixel value of the pixel of interestcomposing the output image. In Step S20, the class tap extractingportion 11, the noise amount tap extracting portion 14, and thepredictive tap extracting portion 17 determines whether or not all thepixels composing the output image are already determined as the pixelsof interest, respectively.

It is determined in Step S20 that all the pixels composing the outputimage are not yet determined as the pixels of interest, respectively,the operation returns back to the processing in Step S11, and theprocessing described above is repeatedly executed.

On the other hand, it is determined in Step S20 that all the pixelscomposing the output image are already determined as the pixels ofinterest, respectively, in Step S21, the predicting portion 18 outputsthe output image composed of the pixel values generated based on thepredictive arithmetic operation, thereby completing the operation.

As described above, the image processing apparatus 10 generates thepredictive coefficient W by using the processing coefficients for therespective classes obtained based on the correlation of the class tapobtained from the learning which will be described later, and theestimate noise amounts σ′. Therefore, the optimal predictive coefficientW corresponding to the correlation of the class tap, and the estimatenoise amounts σ′ can be generated without explosively increasing thenumber of classes. As a result, the image processing apparatus 10 canexecute the highly precise noise removing processing by using thepredictive coefficient W, thereby generating the output image, havingthe high image quality, from which the luminance dependency noise isremoved.

In addition, according to the experiments, an S/N ratio of the outputimage in the image processing apparatus 10 becomes larger than that ofthe output image obtained from the class classifying adaptationprocessing in the related art by using the predictive coefficientsobtained from the learning made for the classes obtained through theclassification by using the correlation of the class tap, and theestimate noise amounts σ′. For example, when the number of pixel valuescomposing the predictive coefficient and the noise amount tap is 9,according to the experiments, the former is 36.5 and the latter is 35.6.As a result, it is understood that the image processing apparatus 10 cangenerate the output image having the higher image quality.

Next, a description will be given with respect to the learning for theprocessing coefficients used to generate the predictive coefficient W inthe image processing apparatus 10. The learning for the processingcoefficients, for example, is carried out by utilizing a least-squaremethod.

Specifically, a true value of a pixel value of a pixel of an outputimage in a k-th sample is represented by y_(k), an n-dimensional vectorX of an input pixel composing a predictive tap about the pixels of theoutput image in the k-th sample is represented by X_(k) (X_(k)=(x_(k0),x_(k1), . . . , x_(kn))), and the least-square method, for example, isadopted as the norm representing that the predictive coefficient W isthe optimal one. In this case, a minimization function Q is expressed byExpression (6):

$\begin{matrix}{Q = {\sum\limits_{k = 1}^{N}\left( {y_{k} - {WX}_{k}} \right)^{2}}} & (6)\end{matrix}$

where N is the number of samples used in set learning of the pixelvalues y_(k) of the output image, and an n-dimensional vector of theinput image composing the predictive tap about the pixel values y_(k)(the number of samples for the learning).

A minimum value (local minimum value) of the minimization function Qexpressed by Expression (6) is given by a processing coefficient inwhich a value obtained by partially differentiating the minimizationfunction Q by all variable numbers is made zero. Therefore, a linearsimultaneous equation of an addition matrix shown in FIG. 7 which isstructured so that the minimization function Q is partiallydifferentiated by all the variable numbers, and the resulting valuebecomes zero is solved, thereby obtaining the optimal processingcoefficient.

The addition matrix shown in FIG. 7 is divided into small blocks (smallblocks each composed of a matrix of n×n in the case of a matrix of aleft-hand side of a left member, and small blocks each composed of amatrix of n×1 in the case of each of a matrix of a right-hand side of aleft member, and a matrix of the right member). Each of the small blocksof the matrix of the left-hand side of the left member, and the matrixof the right member is structured by multiplying elements of theaddition matrix corresponding to the linear predictive arithmeticoperation in the class classifying adaptation processing in the relatedart by the values of the estimate noise amounts σ′ corresponding to thepositions of the small blocks. It is noted that suffixes i and j (0≦i,j≦n) represent the positions of the pixels corresponding to the pixelvalues within the predictive tap.

The addition matrix shown in FIG. 7 is generated every class and thusthe optimal processing coefficient is obtained every class.

According to the class classifying adaptation processing executed by theimage processing apparatus 10, the matrix arithmetic operation forExpression (5) is carried out by using the processing coefficients forthe respective classes obtained in the manner described above, therebygenerating the predictive coefficient W. Also, the predictive arithmeticoperation for Expression (3) is carried out by using the resultingpredictive coefficient W, thereby converting the input image into theoutput image.

FIG. 8 is a block diagram showing an example of a configuration of alearning apparatus 30 for learning the processing coefficients used bythe image processing apparatus 10 shown in FIG. 1.

The learning apparatus 30 shown in FIG. 8 is composed of a learning pairstoring portion 31, a class tap extracting portion 32, a classclassifying portion 33, a noise amount tap extracting portion 34, anoise amount arithmetically operating portion 35, a predictive tapextracting portion 36, a normal equation generating portion 37, acoefficient generating portion 38, and a coefficient storing portion 39.

In the learning apparatus 30, the learning pair storing portion 31stores therein a set of an image containing therein a luminancedependency noise and corresponding to an input image in the imageprocessing apparatus 10 as a student in learning for the processingcoefficients (hereinafter referred to as “a student image”), and animage corresponding to an ideal output image into which the input imageis converted as a teacher (hereinafter referred to as “a teacher image”)in the form of a learning pair.

In addition, the learning pair storing portion 31 outputs the data onthe student image of the learning pair to each of the class tapextracting portion 32, the noise amount tap extracting portion 34, andthe predictive tap extracting portion 36. Also, the learning pairstoring portion 31 outputs the data on the teacher image of the learningpair to the normal equation generating portion 37.

The class tap extracting portion 32 successively determines the pixelscomposing the teacher image as the pixels of interest similarly to thecase of the class tap extracting portion 11 shown in FIG. 1. Also, theclass tap extracting portion 32 extracts the pixel values of a pluralityof pixels, within the student image, corresponding to the position ofthe pixel of interest, and the peripheral positions of the position ofthe pixel of interest in the form of the class tap from the studentimage. In this case, the pixel values of a plurality of pixels withinthe student image are used to classify the pixels of interest into theclasses. The class tap extracting portion 32 supplies the data on theresulting class tap to the class classifying portion 33.

The class classifying portion 33 classifies the pixels of interest intothe classes in correspondence to the feature of the class tap suppliedthereto from the class tap extracting portion 32 similarly to the caseof the class classifying portion 12 shown in FIG. 1, thereby generatingthe classes corresponding to the pixels of interest. The classclassifying portion 33 supplies the data on the classes to the normalequation generating portion 37.

The noise amount tap extracting portion 34 successively determines thepixels composing the teacher image as the pixels of interest,respectively, the case of the class tap extracting portion 32. Also, thenoise amount tap extracting portion 34 extracts the pixel values of aplurality of pixels, within the student image, corresponding to theposition of the pixel of interest, and the peripheral positions of theposition of the pixel of interest in the form of the noise amount tapfrom the student image similarly to the case of the noise amount tapextracting portion 14 shown in FIG. 1. In this case, the pixel values ofa plurality of pixels within the student image are used toarithmetically operate the estimate noise amount σ′ corresponding to thepixel of interest. The noise amount tap extracting portion 34 suppliesthe data on the noise amount tap thus extracted to the noise amountarithmetically operating portion 35.

The noise amount arithmetically operating portion 35 arithmeticallyoperates the estimate noise amount σ′ corresponding to the pixel ofinterest from the noise amount tap supplied thereto from the noiseamount tap extracting portion 34 in accordance with Expression (2)similarly to the case of the noise amount arithmetically operatingportion 15 shown in FIG. 1. Also, the noise amount arithmeticallyoperating portion 35 supplies the data on the estimate noise amount σ′corresponding to the pixel of interest to the normal equation generatingportion 37.

The predictive tap extracting portion 36 successively determines thepixels composing the teacher image as the pixels of interest,respectively, similarly to the case of each of the class tap extractingportion 32, and the noise amount tap extracting portion 34. Also, thepredictive tap extracting portion 36 extracts the pixel values of aplurality of pixels within the student image corresponding to theposition of the pixel of interest, and the peripheral positions of theposition of the pixel of interest as the predictive tap from the studentimage similarly to the case of the predictive tap extracting portion 17shown in FIG. 1. In this case, the pixel values of a plurality of pixelswithin the student image are used to predict the pixel of interest.Also, the predictive tap extracting portion 36 supplies the data on thepredictive tap thus extracted to the normal equation generating portion37.

The normal equation generating portion 37 generates the addition matrix(refer to FIG. 7) in the form of the normal equation. In this case, theaddition matrix is obtained by performing the addition by using theestimate noise amount σ′ supplied from the noise amount arithmeticallyoperating portion 35, the predictive tap supplied from the predictivetap extracting portion 36, and the teacher image inputted from thelearning pair storing portion 31 every class supplied from the classclassifying portion 33.

Specifically, the normal equation generating portion 37 substitutes thepixel values of the student image composing the predictive tap in thek-th sample as X_(k) (X_(k)=(x_(k0), x_(k1), . . . , x_(kn))) into theaddition matrix shown in FIG. 7 for the classes. In addition, the normalequation generating portion 37 substitutes the pixel values of the pixelof interest of the teacher image in the k-th sample in the form of y_(k)into the addition matrix shown in FIG. 7. Also, the normal equationgenerating portion 37 substitutes the estimate noise amounts σ′corresponding to the pixels of interest, respectively, into the additionmatrix shown in FIG. 7. As a result, the normal equation generatingportion 37 generates the normal equation.

It is noted that the addition matrix, as described above, is such thatthe minimization function Q expressed by Expression (6) is made zero.Therefore, it can be the that the normal equation generated by thenormal equation generating portion 37 is an equation for solving anexpression corresponding to Expression (3) for generation of the teacherimage based on the multiplication of the predictive coefficient Wobtained from both the estimate noise amounts σ′ and the processingcoefficients, and the predictive tap of the student image, therebyobtaining the processing coefficients. The normal equation generatedfrom the normal equation generating portion 37 is supplied to thecoefficient generating portion 38.

The coefficient generating portion 38 solves the normal equationsupplied thereto from the normal equation generating portion 37, therebygenerating the processing coefficients. Also, the coefficient generatingportion 38 instructs the coefficient storing portion 39 to store thereinthe processing coefficients thus generated. The processing coefficientswhich are learned in the manner as described above, and are then storedin the coefficient storing portion 39 are stored in the coefficientstoring portion 13 shown in FIG. 1, and are used in the image processingapparatus 10.

Next, learning processing executed by the learning apparatus 30 shown inFIG. 8 will be described with reference to a flow chart of FIG. 9.

Firstly, in Step S30, the learning pair storing portion 31 outputs thelearning pair which is not yet outputted of the learning pairs storedtherein. Specifically, the learning pair storing portion 31 inputs thedata on the student image of the learning pair to each of the class tapextracting portion 32, the noise amount tap extracting portion 34, andthe predictive tap extracting portion 36. On the other hand, thelearning pair storing portion 31 inputs the data on the teacher image ofthe learning pair to the normal equation generating portion 37.

Next, in Step S31, the class tap extracting portion 32, the noise amounttap extracting portion 34, and the predictive tap extracting portion 36determine one of the pixels, of a plurality of pixels composing theteacher image, which are not yet determined as the pixels of interest asthe pixel of interest similarly to the case of the class tap extractingportion 11 shown in FIG. 1.

In Step S32, the class tap extracting portion 32 extracts the class tapcorresponding to the pixel of interest from the student image, andsupplies the data on the class tap thus extracted to the classclassifying portion 33. In Step S33, the class classifying portion 33classifies the pixel of interest into the corresponding one of theclasses in correspondence to the feature of the class tap suppliedthereto from the class tap extracting portion 32 similarly to the caseof the class classifying portion 12 shown in FIG. 1, thereby generatingthe class for the pixel of interest. The class classifying portion 33supplies the data on the class thus generated to the normal equationgenerating portion 37.

In Step S34, the noise amount tap extracting portion 34 extracts thenoise amount tap corresponding to the pixel of interest from the studentimage, and supplies the data on the noise amount tap thus extracted tothe noise amount arithmetically operating portion 35 similarly to thecase of the noise amount tap extracting portion 14 shown in FIG. 1.

In Step 35, the noise amount arithmetically operating portion 35arithmetically operates the estimate noise amount σ′ corresponding tothe noticed image from the noise amount tap supplied thereto from thenoise amount tap extracting portion 34 in accordance with Expression (2)similarly to the case of the noise amount arithmetically operatingportion 15 shown in FIG. 1. Also, the noise amount arithmeticallyoperating portion 35 supplies the data on the estimate noise amount σ′to the normal equation generating portion 37.

In Step S36, the predictive tap extracting portion extracts thepredictive tap corresponding to the pixel of interest from the studentimage similarly to the case of the predictive tap extracting portion 17shown in FIG. 1, and supplies the data on the predictive tap thusextracted to the normal equation generating portion 37.

In Step S37, the normal equation generating portion carries out theaddition for the addition matrix every class supplied thereto from theclass classifying portion (refer to FIG. 7) by using the estimate noiseamounts σ′ supplied thereto from the noise amount arithmeticallyoperating portion 35, the predictive tap supplied thereto from thepredictive tap extracting portion 36, and the teacher image inputtedthereto from the learning pair storing portion 31.

In Step S38, the class tap extracting portion 32, the noise amount tapextracting portion 34, and the predictive tap extracting portion 36determine whether or not all the pixels composing the teacher image arealready determined as the pixels of interest. When it is determined inStep S38 that all the pixels composing the teacher image are not yetdetermined as the pixels of interest, the operation returns back to theprocessing in Step S31, and the processing described above is repeatedlyexecuted.

On the other hand, when it is determined in Step S38 that all the pixelscomposing the teacher image are already determined as the pixels ofinterest, in Step S39, the learning pair storing portion 31 determineswhether or not the processing from Step S30 to Step S38 is alreadyexecuted for all the learning pairs, that is, whether or not all thelearning pairs stored therein are already outputted. When it isdetermined in Step S39 that the processing from Step S30 to Step S38 isnot yet executed for all the learning pairs, the operation returns backto the processing in Step S30, and the processing described above isrepeatedly executed.

On the other hand, when it is determined in Step S39 that all thelearning pairs stored therein are already outputted, the normal equationgenerating portion 37 supplies the data on the normal equation generatedby carrying out the addition in Step S37 to the coefficient generatingportion 38.

Also, in Step S40, the coefficient generating portion 38 generates theprocessing coefficients by solving the normal equation supplied theretofrom the normal equation generating portion 37, and instructs thecoefficient storing portion 39 to store therein the processingcoefficients.

As described above, the learning apparatus 30 learns the optimalprocessing coefficient every class obtained by the classification basedon the correlation of the class tap by using the student imagecontaining therein the luminance dependency noise, and the teacherimage, as the ideal image, from which the luminance dependency noise isremoved. Therefore, the image processing apparatus 10 generates thepredictive coefficient W by using the optimal processing coefficientsand the estimate noise amounts σ′, thereby making it possible togenerate the optimal predictive coefficient W, for removal of theluminance dependency noise, corresponding to the correlation of theclass tap, and the estimate noise amounts σ′ without explosivelyincreasing the number of classes. As a result, the image processingapparatus 10 can generate the output image, having the high imagequality, from which the luminance dependency noise is removed.

It is noted that although in the above description, the noticed imagesare classified into the classes in correspondence to the correlation ofthe class tap, the noticed images may not be classified.

Next, a series of processing described above can be executed by eitherthe hardware or the software. When the series of processing describedabove is executed by the software, a program composing the software isinstalled from a program recording medium either in a computerincorporated in a dedicated hardware, or, for example, in a generalpurpose personal computer or the like which can execute variousfunctions by installing therein various programs.

FIG. 10 shows an example of a configuration of the hardware in acomputer 300 for executing the series of processing described above inaccordance with a program.

In the computer 300, a Central Processing Unit (CPU) 301, a Read OnlyMemory (ROM) 302, and a Random Access Memory (RAM) 303 are connected toone another through a bus 304.

In addition, an I/O interface 305 is connected to the bus 304. An inputportion 306, an output portion 307, a storing portion 308, acommunication portion 309, and a drive 310 are also connected to the I/Ointerface 305. In this case, the input portion 306 is composed of areceiving portion or the like for receiving an instruction transmittedthereto from a keyboard, a mouse, and a microphone, a remote controller,or the like. The output portion 307 is composed of a display device, aspeaker or the like. The storing portion 308 is composed of a hard disc,a nonvolatile memory or the like. Also, the drive 310 drives a removablemedia 311 as a package media. In this case, the removable media 311 iscomposed of a magnetic disc (including a flexible disc), an optical disc(such as a Compact Disc-Read Only Memory (CD-ROM), or a DigitalVersatile Disc (DVD)), a magneto optical disc, or a semiconductormemory.

With the computer 300 configured in the manner as described above, theCPU 301 loads the program, for example, stored in the storing portion308 into the RAM 303 through the I/O interface 305 and the bus 304,thereby executing the series of processing described above.

The program which the CPU 301 of the computer 300 executes, for example,is recorded in the removable media 311, or is provided through a wiredor wireless transmission medium such as a Local Area Network (LAN), theInternet or a digital satellite-based broadcasting.

Also, the program can be installed in the storing portion 308 throughthe I/O interface 305 by equipping the drive 310 with the removablemedia 311. In addition, the program can be received at the communicationportion 309 through the wired or wireless transmission media to beinstalled in the storing portion 308. In addition thereto, the programcan be previously installed either in the ROM 302 or in the storingportion 308.

It is noted that the program which the CPU 301 of the computer 300executes may be either a program in accordance with the processing isexecuted in a time series manner so as to follow the order explained inthis specification, or a program in accordance with which the processingis executed at a necessary timing when a call is made.

In addition, the embodiment of the present invention is by no meanslimited to the embodiments described above, and various changes thereofcan be made without departing from the gist of the present invention.

It should be understood by those skilled in the art that variousmodifications, combinations, sub-combinations and alterations may occurdepending on design requirements and other factors insofar as they arewithin the scope of the appended claims or the equivalents thereof.

1. An image processing apparatus for converting a first image into asecond image having higher image quality than that of the first image,comprising: first pixel value extracting means for extracting aplurality of pixel values, within the first image, corresponding to aposition of a pixel of interest, and peripheral positions of theposition of the pixel of interest within the second image; estimatenoise amount arithmetically operating means for obtaining estimate noiseamounts for the plurality of pixel values extracted by the first pixelvalue extracting means, respectively; processing coefficient generatingmeans for generating second processing coefficients in accordance withan arithmetic operation for first processing coefficients previouslylearned from a normal equation, and the estimate noise amounts obtainedfor the plurality of pixel values, respectively, within the first image,the normal equation being obtained based on a relational expression forgenerating a teacher image corresponding to the second image havinghigher image quality than that of a student image in accordance with anarithmetic operation for the second processing coefficients obtained inaccordance with estimate noise amounts about the pixel values within thestudent image corresponding to the first image, and the first processingcoefficients, and the student image; second pixel value extracting meansfor extracting a plurality of pixel values, within the first image,corresponding to a position of a pixel of interest, and peripheralpositions of the position of the pixel of interest within the secondimage; and predicting means for generating a pixel value of the pixel ofinterest within the second image in accordance with an arithmeticoperation for the plurality of pixel values extracted by the secondpixel value extracting means, and the second processing coefficients. 2.The image processing apparatus according to claim 1, wherein therelational expression is an expression representing a relation in whichthe N second processing coefficients are obtained in accordance with amatrix arithmetic operation for the N estimate noise amounts obtainedfrom the pixel values of the N pixels, within the student image,corresponding to the position of the pixel of interest, and theperipheral positions of the position of the pixel of interest within theteacher image, and the first processing coefficients expressed in a formof a matrix of N×N, and the pixels of interest within the teacher imageare generated in accordance with a linear combination of the N secondprocessing coefficients, and the pixel values of the N pixels within thestudent image.
 3. The image processing apparatus according to claim 1,wherein the estimate noise amount is obtained in a form of a quadraticexpression of the pixel values within the student image.
 4. The imageprocessing apparatus according to claim 1, further comprising classclassifying means for generating a class for the pixel of interest inaccordance with a feature of a class tap composed of the plurality ofpixel values, within the first image, corresponding to the position ofthe pixel of interest, and the peripheral positions of the position ofthe pixel of interest within the second image; wherein the processingcoefficient generating means generates the second processingcoefficients in accordance with an arithmetic operation for the firstprocessing coefficients, of the class generated by the class classifyingmeans, of the first processing coefficients for the classes previouslylearned from the normal equation for the classes, and the estimate noiseamounts for the plurality of pixel values within the first image.
 5. Animage processing method for use in an image processing apparatus forconverting a first image into a second image having higher image qualitythan that of the first image, the image processing method comprising thesteps of: extracting a plurality of pixel values, within the firstimage, corresponding to a position of a pixel of interest, andperipheral positions of the position of the pixel of interest within thesecond image; obtaining estimate noise amounts for the plurality ofpixel values, respectively; generating second processing coefficients inaccordance with an arithmetic operation for first processingcoefficients previously learned from a normal equation, and the estimatenoise amounts obtained for the plurality of pixel values, respectively,within the first image, the normal equation being obtained based on arelational expression for generating a teacher image corresponding tothe second image having higher quality than that of a student image inaccordance with an arithmetic operation for the second processingcoefficients obtained in accordance with estimate noise amounts aboutthe pixel values within the student image corresponding to the firstimage, and the first processing coefficients, and the student image;extracting a plurality of pixel values, within the first image,corresponding to a position of a pixel of interest, and peripheralpositions of the position of the pixel of interest within the secondimage; and generating a pixel value of the pixel of interest within thesecond image in accordance with an arithmetic operation for theplurality of pixel values thus extracted, and the second processingcoefficients.
 6. A program in accordance with which a computer executesimage processing for converting a first image into a second image havinghigher image quality than that of the first image, the programcomprising the steps of: extracting a plurality of pixel values, withinthe first image, corresponding to a position of a pixel of interest, andperipheral positions of the position of the pixel of interest within thesecond image; obtaining estimate noise amounts for the plurality ofpixel values, respectively; generating second processing coefficients inaccordance with an arithmetic operation for first processingcoefficients previously learned from a normal equation, and the estimatenoise amounts obtained for the plurality of pixel values, respectively,within the first image, the normal equation being obtained based on arelational expression for generating a teacher image corresponding tothe second image having higher quality than that of a student image inaccordance with an arithmetic operation for the second processingcoefficients obtained in accordance with estimate noise amounts aboutthe pixel values within the student image corresponding to the firstimage, and the first processing coefficients, and the student image;extracting a plurality of pixel values, within the first image,corresponding to a position of a pixel of interest, and peripheralpositions of the position of the pixel of interest within the secondimage; and generating a pixel value of the pixel of interest within thesecond image in accordance with an arithmetic operation for theplurality of pixel values thus extracted, and the second processingcoefficients.
 7. A learning apparatus, comprising: normal equationgenerating means for obtaining estimate noise amounts from pixel valueswithin a student image containing therein a noise having noisedependency, obtaining second processing coefficients in accordance withan arithmetic operation for the estimate noise amounts, and firstprocessing coefficients, and generating a normal equation by using thepixel values of the student image, and pixel values of the teacherimage, in order to solve a relational expression for generating theteacher image having higher image quality than that of the studentimage, in accordance with an arithmetic operation for the secondprocessing coefficients and the student image; and coefficientgenerating means for generating the first processing coefficients bysolving the normal equation.
 8. The learning apparatus according toclaim 7, wherein the relational expression is an expression representinga relation in which the N second processing coefficients are obtained inaccordance with a matrix arithmetic operation for the N estimate noiseamounts obtained from the pixel values of the N pixels, within thestudent image, corresponding to the position of the pixel of interest,and the peripheral positions of the position of the pixel of interestwithin the teacher image, and the first processing coefficientsexpressed in a form of a matrix of N×N, and the pixels of interestwithin the teacher image are generated in accordance with a linearcombination of the N second processing coefficients, and the pixelvalues of the N pixels within the student image.
 9. The learningapparatus according to claim 7, wherein the estimate noise amount isobtained in a form of a quadratic expression of the pixel values withinthe student image.
 10. The learning apparatus according to claim 7,further comprising class classifying means for generating a class forthe pixel of interest in accordance with a feature of a class tapcomposed of the plurality of pixel values, within the student imagecorresponding to the position of the pixel of interest, and theperipheral positions of the position of the pixel of interest within theteacher image; wherein the normal equation generating means generatesthe normal equation every class generated by the class classifying meansby using the pixel values of the student image, and the pixel value ofthe pixel of interest.
 11. An image processing apparatus for convertinga first image into a second image having higher image quality than thatof the first image, comprising: a first pixel value extracting sectionconfigured to extract a plurality of pixel values, within the firstimage, corresponding to a position of a pixel of interest, andperipheral positions of the position of the pixel of interest within thesecond image; an estimate noise amount arithmetically operating sectionconfigured to obtain estimate noise amounts for the plurality of pixelvalues extracted by the first pixel value extracting section,respectively; a processing coefficient generating section configured togenerate second processing coefficients in accordance with an arithmeticoperation for first processing coefficients previously learned from anormal equation, and the estimate noise amounts obtained for theplurality of pixel values, respectively, within the first image, thenormal equation being obtained based on a relational expression forgenerating a teacher image corresponding to the second image havinghigher image quality than that of a student image in accordance with anarithmetic operation for the second processing coefficients obtained inaccordance with estimate noise amounts about the pixel values within thestudent image corresponding to the first image, and the first processingcoefficients, and the student image; a second pixel value extractingsection configured to extract a plurality of pixel values, within thefirst image, corresponding to a position of a pixel of interest, andperipheral positions of the position of the pixel of interest within thesecond image; and a predicting section configured to generate a pixelvalue of the pixel of interest within the second image in accordancewith an arithmetic operation for the plurality of pixel values extractedby the second pixel value extracting section, and the second processingcoefficients.
 12. A learning apparatus, comprising: a normal equationgenerating section configured to obtain estimate noise amounts frompixel values within a student image containing therein a noise havingnoise dependency, obtaining second processing coefficients in accordancewith an arithmetic operation for the estimate noise amounts, and firstprocessing coefficients, and generating a normal equation by using thepixel values of the student image, and pixel values of the teacherimage, in order to solve a relational expression for generating theteacher image having higher image quality than that of the studentimage, in accordance with an arithmetic operation for the secondprocessing coefficients and the student image; and a coefficientgenerating section configured to generate the first processingcoefficients by solving the normal equation.